Problem: Rewrite as a simplified fraction. ${0.\overline{97} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 97.9797...\\ 1x &= 0.9797...\end{align*}}$ Subtracting the two equations, we have: ${99x = 97}$ ${x = \dfrac{97}{99}} $